Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
774 conjugacy classes of subgroups; only the 206 normal subgroups are shown.
This group has 774 conjugacy classes of subgroups — too many to draw. Only its 206 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#19153904 | C2 | semidirect |
| 2. #26042254 | C2 | semidirect |
| 3. #26042250 | C2 | semidirect |
| 4. D181⋊(C22⋊C8) | C2 | semidirect |
| 7. C2×#15668459 | C22 | semidirect |
| 8. C2×D181⋊C8 | C22 | semidirect |
| 9. #19153873 | C22 | semidirect |
| 10. #19153873 | C22 | semidirect |
| 69. C22×C181 | #131 | semidirect |
| 88. C181 | #2880 | semidirect |
| 165. C22 | #19153904 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153904 | 2 |
| #26042254 | 2 |
| #26042250 | 2 |
| D181⋊(C22⋊C8) | 2 |
| C22×#15668450 | 2 |
| #2880 | 181 |